The Glade 4.0

DDWFTTW = Directly Downwind Faster Than The Wind

A team has created a wind-powered car that can travel directly down wind over 3x times the speed of the wind. The way it works is totally counter-intuitive and I'm not sure I understand it yet (and there are plenty of doubters)--the wheels drive the propeller. Lots of discussions on force vectors and such. You guys might find it interesting.

http://blog.makezine.com/archive/2010/1 ... black.html

Oooh. Neat. I'll have to dive in tomorrow.

I love wind-powered transportation.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

My two biggest fascinations lately have been wireless electrical power transfer and varying constants. I was reading this book and got to the chapter where he was discussing the fine structure constant, and it got me wondering why math constants seem to be sacred. If alpha can change over the universe, why not pi or e? What would round things look like if pi were a little closer to four, or a little closer to three? How would bacteria and other microbial life proliferate if e lost some weight?

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Buckle your pants or they might fall down.

Don't be hatin' on π

It's perfect, just as it is.

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In time, this too shall pass.

Maybe if pi put on a few pounds, human suffering would disappear.

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Buckle your pants or they might fall down.

I don't think that's possible. How could you have a circular orbit, for example, if pi is four? If you attach a ball to a chain and swing it around, is the chain going to change lengths?

How would waves propagate? How would any periodic function work? How would vectors get broken up into their perpendicular components in a rectilinear coordinate system? If you change pi, lots of stuff get wacky that aren't even based off of circles, but that involve trigonometric functions.

So the chain's length stays constant. However, the ball is now tracing out a longer path in the same amount of time. The ball is going faster, and the tension in the chain increases. If pi gets bigger than 5, the chain breaks.

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Buckle your pants or they might fall down.

If pi is bigger, there is more for me to eat.....mmmmmmm pumpkin

The only way to change π is to change the relationship between the circumference and the diameter of a circle.

I suggest a contacting a lawyer. They've always been able to change my relationships...

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In time, this too shall pass.

Funny you should say this...

I heard (and I'm not feeling like looking it up to verify, but the source was credible) that when the US government places survey markers defining sections, that the distance between the markers is defined by law to be one mile. Naturally, there are errors, so if two markers are, say a mile and tenth apart, they by the power and force of law become one mile. So if you want to change pi, just find an appropriate section to use as your reference mile, measure circumference, divide and there you have it: a weightier pi with the full backing of the US government.

Lonedar -- that only works if you use two different sections for the circumference and the radius/diameter.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

You don't need to. The diameter is one mile, by law. When you measure the circumference with your roller-measurer thingy, you just might get 3.2 miles, and a weightier pi.

Ah, I see. You're not recalibrating your roller measurer thingy to measure the circumference. So my point stands, you're using two different standards; however you accurately point out that you don't need two sections, just one section and a "real" mile.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

Kaffis, I thing you are missing the awesome power of the US government here. If there was a one mile standard officially recognized by the National Institute of Standards and Technology...every section line would be exactly that length because the law says they are. Therefore there is only one standard, but somehow through the power of legislation you can get heavy pi. And its all legal.

No, no. I'm following you. But it does involve "measuring" by two different segments. You can get a light pi, too. But they taste bad.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

I support legal heavy pi!

While we're on the subject of abstract mathy stuffs, this is a good a time as any to bring up this idea that came up the other day... I'm pretty confident I didn't invent any new calculus, but my professor (who isn't a PhD, for whatever that's worth) couldn't come up with an answer for me when I asked him about it. Either it exists and has next to no use, or more likely I made some assumption somewhere that doesn't work.

Essentially it deals with derivatives of equations with base 'e', which have a rather unique property in that the function and its derivative are the same when it's simply f(x) = e^x.

My logic seems to result in a simple formula not only for the first, second, or third derivative of an equally simple formula, as well as a slightly more complicated e^(nx) where n is some constant, such as 3 in the example below... but it seems to devolve into crazyland when it seems to work to find (in addition to those first, second, and third derivatives) the one and a halfth© derivative, three and three quartersth© derivative, pi'th© derivative, and so on.

Apologies for those not using Glade theme! I was afraid to use transparent background for fear of black text on potential black backgrounds!



My brain can't make heads or tails of what it would mean, but it seems to work. There are other things in mathematics that my brain can't wrap itself around anyway, so that's hardly a damning quality. Even simple calculators don't balk at 3 to the 1.5th power, but that has to be kinda mind-blowing to someone thinking exponents means to multiply the base by itself that many times. I've done a little searching about for something along the lines of "non-integer order derivatives" and the like but haven't come up with anything relevant beyond some programmer coming to a similar conclusion as an afterthought... and that's hardly a quality source!

So... do I get any clever points for stumbling upon existing math or did I just make a dumb assumption somewhere? :p When I was typing up the graphic I am feeling less than secure about my n^c part of it (as per above paragraph), but I can't say I am too fresh in my math basics. It's been 10 years since I had a calculus class and 8 since I've had a math class of any kind.

Fractional Calculus, Noggel.

Granted, I had to look it up, as I've never had occasion to work with it, to my recollection. But yours is an extreme (in the sense that not only is it fractional, but it is so essentially using a non-rational fraction) case of this, it appears.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

I haven't paid any attention to the alpha thing except as it relates to c. Unfortunately some Young Earth Creationists have jumped all over the possibility that c might have changed so it'll probably get short shrift from physicists.

I've been playing with magnetism and Lenz's law lately. I never took a physics class that involved magnetism and I feel like I missed out. I am easily amused and I've been fascinated by the surprising results of rolling a rare-earth magnetic ball down a copper pipe.

BTW, rare earth magnets are crazy strong. I had no idea.

Doubtful. Scientific "constants" being dependent on your location in time and space supports the notion of string theorists that you can have bubble universes and such. It's also, frankly, too cool an idea to die because some religious wackjobs got excited.That isn't quite how it works. C = 2πr can still be true. You just have a bigger circumference than you used to. It sounds like it's totally impossible, but that's exactly what may be the case with the fine structure constant (and possibly others). The number changes, but the formula does not. The average person's familiarity with pi makes it a good example to use to explain the concept, too. "That can't be!" It's that mind-boggling, yes. It's also hardly the craziest idea in the past hundred years of physics, and some of the most batshit of those turned out to be true. Space isn't flat, and a second for you is different than a second for me. That's far more **** up than waking up tomorrow and having pi equal 3.1392.

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Buckle your pants or they might fall down.

Einstein's General Relativity predicts that space is non-Euclidean around mass(Riemannian geometry), so if one could measure the circumference and the diameter of a circle on earth accurately enough it wouldn't be pi anyway, so we already need to put on the crazy glasses.

Ah, cool! I can see why they sort of skip over that in basic calculus courses... not exactly the most practical of applications. I can rest well now, though!

You can have a (4 - 3i)th derivative, too.

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Buckle your pants or they might fall down.

Is that how you calculate the rate of change of curvature of space at any given point in the Cheshire Cat's grinning process?

You math people and your i's.

No, it wouldn't. Engineers would increase their factor of safety to compensate for your funky pi.

Engineers are awesome that way.

Engineers > US Government > Math > Physics > Funky Pi

But corporations driving shareholder value by maximizing performance while minimizing costs have required their engineers to cut out deadweight (read as "unnecesarily large factors of safety") to reduce weight and cost and improve schedule.

Corporate Bean Counters > Engineers > US Government > Math > Physics > Funky Pi